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On differential equations and inclusions with mean derivatives on a compact manifold

S.V. Azarina, Yu.E. Gliklikh (2007)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

We introduce and investigate a new sort of stochastic differential inclusions on manifolds, given in terms of mean derivatives of a stochastic process, introduced by Nelson for the needs of the so called stochastic mechanics. This class of stochastic inclusions is ideologically the closest one to ordinary differential inclusions. For inclusions with forward mean derivatives on manifolds we prove some results on the existence of solutions.

Optimization of Discrete-Time, Stochastic Systems

Papageorgiou, Nikolaos (1995)

Serdica Mathematical Journal

* This research was supported by a grant from the Greek Ministry of Industry and Technology.In this paper we study discrete-time, finite horizon stochastic systems with multivalued dynamics and obtain a necessary and sufficient condition for optimality using the dynamic programming method. Then we examine a nonlinear stochastic discrete-time system with feedback control constraints and for it, we derive a necessary and sufficient condition for optimality which we then use to establish the existence...

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